Existence for dislocation-free finite plasticity

¹ Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
² Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes, v. Ferrata 1, 27100 Pavia, Italy

^* Corresponding author: ulisse.stefanelli@univie.ac.at

Received: 9 October 2017
Accepted: 13 February 2018

Abstract

This note addresses finite plasticity under the constraint that plastic deformations are compatible. In this case, the total elastoplastic deformation of the medium is decomposed as y = y_e ○ y_p, where the plastic deformation y_p is defined on the fixed reference configuration and the elastic deformation y_e is a mapping from the varying intermediate configuration y_p(Ω). Correspondingly, the energy of the medium features both Lagrangian (plastic, loads) and not Lagrangian contributions (elastic).

We present a variational formulation of the static elastoplastic problem in this setting and show that a solution is attained in a suitable class of admissible deformations. Possible extensions of the result, especially in the direction of quasistatic evolutions, are also discussed.